12,326 research outputs found
Renormalization of a Lorentz invariant doubled worldsheet theory
Manifestly T-duality covariant worldsheet string models can be constructed by
doubling the coordinate fields. We describe the underlying gauge symmetry of a
recently proposed Lorentz invariant doubled worldsheet theory that makes half
of the worldsheet degrees of freedom redundant. By shifting the Lagrange
multiplier, that enforces the gauge fixing condition, the worldsheet action can
be cast into various guises. We investigate the renormalization of this theory
using a non-linear background / quantum split by employing a normal coordinate
expansion adapted to the gauge-fixed theory. The propagator of the doubled
coordinates contains a projection operator encoding that half of them do not
propagate. We determine the doubled target space equations of motion by
requiring one-loop Weyl invariance. Some of them are generalizations of the
conventional sigma model beta-functions, while others seem to be novel to the
doubled theory: In particular, a dilaton equation seems related to the strong
constraint of double field theory. However, the other target space field
equations are not identical to those of double field theory.Comment: 32 pages; v2: motivation and discussion expanded, references adde
Dispersionless Toda hierarchy and two-dimensional string theory
The dispersionless Toda hierarchy turns out to lie in the heart of a recently
proposed Landau-Ginzburg formulation of two-dimensional string theory at
self-dual compactification radius. The dynamics of massless tachyons with
discrete momenta is shown to be encoded into the structure of a special
solution of this integrable hierarchy. This solution is obtained by solving a
Riemann-Hilbert problem. Equivalence to the tachyon dynamics is proven by
deriving recursion relations of tachyon correlation functions in the machinery
of the dispersionless Toda hierarchy. Fundamental ingredients of the
Landau-Ginzburg formulation, such as Landau-Ginzburg potentials and tachyon
Landau-Ginzburg fields, are translated into the language of the Lax formalism.
Furthermore, a wedge algebra is pointed out to exist behind the Riemann-Hilbert
problem, and speculations on its possible role as generators of ``extra''
states and fields are presented.Comment: LaTeX 21 pages, KUCP-0067 (typos are corrected and a brief note is
added
Topological Subsystem Codes
We introduce a family of 2D topological subsystem quantum error-correcting
codes. The gauge group is generated by 2-local Pauli operators, so that 2-local
measurements are enough to recover the error syndrome. We study the
computational power of code deformation in these codes, and show that
boundaries cannot be introduced in the usual way. In addition, we give a
general mapping connecting suitable classical statistical mechanical models to
optimal error correction in subsystem stabilizer codes that suffer from
depolarizing noise.Comment: 16 pages, 11 figures, explanations added, typos correcte
Algebraic Structures and Eigenstates for Integrable Collective Field Theories
Conditions for the construction of polynomial eigen--operators for the
Hamiltonian of collective string field theories are explored. Such
eigen--operators arise for only one monomial potential in the
collective field theory. They form a --algebra isomorphic to the
algebra of vertex operators in 2d gravity. Polynomial potentials of orders only
strictly larger or smaller than 2 have no non--zero--energy polynomial
eigen--operators. This analysis leads us to consider a particular potential
. A Lie algebra of polynomial eigen--operators is then
constructed for this potential. It is a symmetric 2--index Lie algebra, also
represented as a sub--algebra of Comment: 27 page
Loop Approach to Lattice Gauge Theories
We solve the Gauss law and the corresponding Mandelstam constraints in the
loop Hilbert space using the prepotential formulation of
dimensional SU(2) lattice gauge theory. The resulting orthonormal and complete
loop basis, explicitly constructed in terms of the prepotential
intertwining operators, is used to transcribe the gauge dynamics directly in
without any redundant gauge and loop degrees of freedom. Using
generalized Wigner-Eckart theorem and Biedenharn -Elliot identity in , we show that the loop dynamics for pure SU(2) lattice gauge theory in
arbitrary dimension, is given by the real symmetric symbols of first kind
(e.g., n=6, 10 for d=2, 3 respectively). The corresponding "ribbon diagrams"
representing SU(2) loop dynamics are constructed. The prepotential techniques
are trivially extended to include fundamental matter fields leading to a
description in terms of loops and strings. The SU(N) gauge group is briefly
discussed.Comment: 32 pages, 9 figures, typos corrected, new references added (to be
published in Nucl. Phys. B
Superconformal Vortex Strings
We study the low-energy dynamics of semi-classical vortex strings living
above Argyres-Douglas superconformal field theories. The worldsheet theory of
the string is shown to be a deformation of the CP^N model which flows in the
infra-red to a superconformal minimal model. The scaling dimensions of chiral
primary operators are determined and the dimensions of the associated relevant
perturbations on the worldsheet and in the four dimensional bulk are found to
agree. The vortex string thereby provides a map between the A-series of N=2
superconformal theories in two and four dimensions.Comment: 22 pages. v2: change to introductio
- …